Ifp > q >0a n dp r<-1<q r , then find th...

If`p > q >0a n dp r<-1

`-(3)/(4)`

0 if n is even

`-(3)/(4)` if n is odd

none of these

Text Solution

Verified by Experts

The correct Answer is:

`=underset(xto1)lim(p-q+qx^(p)-px^(q))/(1-x^(p)-x^(q)+x^(p+q))" "(0/0)`
`=underset(xto1)lim(pqx^(p-1)-pqx^(q-1))/(-px^(p-1)-qx^(q-1)+(p+q)x^(p+q-1))" "(0/0)`
(L'Hospital's rule)
`=underset(xto1)lim(pq(p1)x^(p-2)-pq(q-1)x^(q-2))/(-p(p-1)x^(p-2)-q(q-1)x^(q-2)+(p+q)(p+q-1)x^(p+q-2))`
(L'Hospital's rule)
`=(p-1)/(2)`

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